A Numerical Study of a Nonstationary Solution of the Hasselmann Equation

摘要

The Hasselmann kinetic equation describing nonlinear spectrum evolution of gravity surface waves is investigated for their large periods of time. To solve the problem, the most optimal numerical algorithm of the nonlinear energy transfer computation is used. The nonlinear spectrum evolution is described by various features. The numerical results reveal some general details common for all cases of the spectrum evolution. There are two main domains in the spectrum: a sharply defined peak and a slowly decreasing high-frequency tail. Using the numerical results, an intermediate self-similar frequency spectrum asymptotic approximation is proposed. It is confirmed by field observations of swell spectrum propagating at large distances. This approximation describes the main features of the nonlinear spectrum evolution and provides a preservation of the total energy and wave action.